Download or read book Fourier Analysis of Multigrid Methods for General Systems of PDE written by Per Lötstedt and published by . This book was released on 1990 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Practical Fourier Analysis for Multigrid Methods written by Roman Wienands and published by CRC Press. This book was released on 2004-10-28 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile
Download or read book multigrid methods written by Stephen F. Mccormick and published by CRC Press. This book was released on 2020-08-12 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.
Download or read book An Introduction to Multigrid Methods written by Pieter Wesseling and published by R.T. Edwards, Inc.. This book was released on 2004 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the principles, techniques, applications and literature of multigrid methods. Aimed at an audience with non-mathematical but computing-intensive disciplines and basic knowledge of analysis, partial differential equations and numerical mathematics, it is packed with helpful exercises, examples and illustrations.
Download or read book Multigrid Methods III written by HACKBUSCH and published by Birkhäuser. This book was released on 2013-11-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain a selection of papers presented at the Third European Conference on Multigrid Methods which was held in Bonn on October 1-4, 1990. Following conferences in 1981 and 1985, a platform for the presentation of new Multigrid results was provided for a third time. Multigrid methods no longer have problems being accepted by numerical analysts and users of numerical methods; on the contrary, they have been further developed in such a successful way that they have penetrated a variety of new fields of application. The high number of 154 participants from 18 countries and 76 presented papers show the need to continue the series of the European Multigrid Conferences. The papers of this volume give a survey on the current Multigrid situation; in particular, they correspond to those fields where new developments can be observed. For example, se veral papers study the appropriate treatment of time dependent problems. Improvements can also be noticed in the Multigrid approach for semiconductor equations. The field of parallel Multigrid variants, having been started at the second European Multigrid Conference, is now at the centre of interest.
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Multigrid Methods written by James H Bramble and published by Routledge. This book was released on 2019-01-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
Download or read book The Fourier Analysis of Multigrid type Iterative Methods written by Naomi H. Decker and published by . This book was released on 1987 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Multigrid Methods written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered. Wesseling, P. Unspecified Center ELLIPTIC DIFFERENTIAL EQUATIONS; HYPERBOLIC DIFFERENTIAL EQUATIONS; ITERATIVE SOLUTION; MULTIGRID METHODS; PARTIAL DIFFERENTIAL EQUATIONS; STRUCTURED GRIDS (MATHEMATICS); DATA SMOOTHING; FINITE DIFFERENCE THEORY; FOURIER ANALYSIS; ROBUSTNESS (MATHEMATICS); STRUCTURED PROGRAMMING...
Download or read book Multi Grid Methods and Applications written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
Download or read book Multigrid Methods with Applications to Reservoir Simulation written by and published by . This book was released on 1994 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to obtain Moore-Penrose solutions of the singular systems encountered. For solving anisotropic equations, semicoarsening and line smoothing techniques are used with multiple coarse grid methods to improve convergence. Two-level convergence factors are estimated using multicolor. In the case where each operator has the same stencil on each grid point on one level, exact multilevel convergence factors can be obtained. For solving partial differential equations with discontinuous coefficients, interpolation and restriction operators should include information about the equation coefficients. Matrix-dependent interpolation and restriction operators based on the Schur complement can be used in nonsymmetric cases. A semicoarsening multigrid solver with these operators is used in UTCOMP, a 3-D, multiphase, multicomponent, compositional reservoir simulator. The numerical experiments are carried out on different computing systems. Results indicate that the multigrid methods are promising.
Download or read book Multigrid Methods IV written by P.W. Hemker and published by Birkhäuser. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection from the papers presented at the Fourth European Multigrid Conference, held in Amsterdam, July 6-9,1993. There were 78 registered participants from 14 different countries, and 56 presentations were given. The preceding conferences in this series were held in Cologne (1981, 1985) and in Bonn (1990). Also at the other side of the Atlantic special multigrid conferences are held regularly, at intervals of two years, always in Copper Mountain, Colorado, US. The Sixth Copper Mountain Conference on Multigrid Methods took place in April, 1993. Circumstances prevented us from putting a larger time interval between the Copper and Amsterdam meetings. The next European meeting is planned in 1996, a year later than the next Copper Meeting. When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists. The past twenty years have shown a rapid growth in theoretical understanding, useful applications and widespread acceptance of multi grid in the applied disciplines. Hence, one might ask whether there is still a need today for conferences specially dedicated to multigrid. The general consensus is that the answer is affirmative. New issues have arisen that are best addressed or need also be addressed from a special multigrid point of view.
Download or read book Computational Fluid Dynamics written by Jiri Blazek and published by Butterworth-Heinemann. This book was released on 2015-04-23 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques
Download or read book Geometric Multigrid Methods on Triangular Grids written by Carmen Rodrigo and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the efficient solution of the large sparse systems of equations arising from the discretization of partial differential equations (PDEs) which mathematically model problems encountered in many applications to physics and engineering. This issue is one of the most important aspects in the numerical solution of many problems, and therefore it deserves important attention. With this purpose, our primary interest here is to design efficient finite element geometric multigrid methods on semi-structured triangular grids. To this end, a local Fourier analysis (LFA) on triangular grids is presented in this book, resulting in a very useful tool to choose suitable components of multigrid methods. The practical utility of this approach is illustrated with some examples of scalar and vector problems.
Download or read book Fourier Analysis written by William O. Bray and published by CRC Press. This book was released on 2020-12-17 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
Download or read book Computational Fluid Dynamics Principles and Applications written by Jiri Blazek and published by Elsevier. This book was released on 2001-05-11 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid Dynamics: Principles and Applications
Download or read book Software for Exascale Computing SPPEXA 2016 2019 written by Hans-Joachim Bungartz and published by Springer Nature. This book was released on 2020-07-30 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.
